1. Field of the Invention
The present invention is directed in general to magnetic resonance tomography (MRT) as employed in medicine for examining patients. The present invention is particularly directed to a method for the optimization of k-space trajectories in the location encoding of a magnetic resonance tomography apparatus. An optimally fast sampling of k-matrix achieved as a result thereof leads to the utmost effectiveness of the sequence employed.
2. Description of the Prior Art
MRT is based on the physical phenomenon of nuclear magnetic resonance and has been successfully employed in medicine and biophysics for more than 15 years. In this examination modality, the subject is subjected to a strong, constant magnetic field. As a result thereof, the nuclear spins in the subject align, these having been previously irregularly oriented. Radiofrequency energy can then excite these “ordered” spins to a specific oscillation. This oscillation generates the actual measured signal in MRT that is picked up with suitable reception coils. By utilizing non-uniform magnetic fields, which are generated by gradient coils, the test subject can be spatially encoded in all three spatial directions, which is generally referred to as “location encoding”.
The acquisition of the data in MRT ensues in k-space (frequency domain). The MRT image or spatial domain is obtained from the MRT data in k-space by means of Fourier transformation. The location encoding of the subject that k-space defines ensues by means of gradients in all three spatial directions. A distinction is made between the slice selection (defines an exposure slice in the subject, usually the Z-axis), the frequency encoding (defines a direction in the slice, usually the x-axis) and the phase encoding (defines the second dimension within the slice, usually the y-axis).
First, a slice is selectively excited, for example in the z-direction. The encoding of the location information in the slice ensues by means of a combined phase and frequency encoding with these two aforementioned, orthogonal gradient fields, which, for the example of a slice excited in z-direction, are generated by the gradient coils in the x-direction and the y-direction that have likewise already been mentioned.
FIGS. 2A and 2B show a first possible form of acquiring the data in an MRT scan. The sequence employed is a spin-echo sequence. With such a sequence, the magnetization of the spins is forced into the x-y-plane (in this example) by a slice selection gradient Gz and the spins are excited by means of a 90° RF excitation pulse. Over the course of time (½ TE; TE is the echo time), a dephasing of the magnetization component that together form the cross-magnetization in the x-y-plane Mxy occurs. After a certain time (for example, ½ TE), a 180° RF pulse is emitted in the x-y-plane so that the dephased magnetization components are mirrored without the precession direction and the precession times of the individual magnetization components being varied. After a further time duration TD, the magnetization components again point in the same direction, i.e. a regeneration of the cross-magnetization that is referred to as “rephasing” occurs. The complete regeneration of the cross-magnetization is referred to as spin echo.
In order to measure an entire slice of the examination subject, the imaging sequence is repeated N-times (with a repetition time TR) for various values of the phase encoding gradient, for example Gy, with the frequency of the magnetic resonance signal (spin-echo signal) being sampled in every sequence repetition, and is digitalized and stored N-times in equidistant time steps Δt in the presence of the readout gradient Gx by means of the Δt-clocked ADC (analog-to-digital converter). According to FIGS. 2A and 2B, a number matrix (matrix in k-space or k-matrix) with N×N data points is obtained in this way (a symmetrical matrix having N×N points is only an example; asymmetrical matrices also can be generated). An MR image of the observed slice having a resolution of N×N pixels can be directly reconstructed from this dataset by means of a Fourier transformation. Consistent with the example shown in FIG. 2A, the entries in the k-matrix shown in FIG. 2B have values kx representing the frequency coding and values ky representing the phase coding. (The same applies to FIGS. 3B and 4B discussed below.)
Another method of obtaining the k-matrix is the method of “echo planar imaging” (EPI). The basic idea of this method is to generate a series of echoes in the readout gradient (Gx) in a very short time after a single (selective) RF excitation, these echoes being allocated to different rows in the k-matrix by means of a suitable gradient switching (modulation of the phase encoding gradient Gy). All rows of the k-matrix can be acquired with a single sequence activation in this way. Different versions of the echo planar technique differ only in how the phase encoding gradients are switched, i.e. how the data points of the k-matrix are sampled.
FIG. 3A shows the ideal form of an echo planar pulse sequence using the same designations as in FIG. 2A. The needle-shaped Gy-pulses in the switchover time of the readout gradient Gx lead to the back and forth, row-by-row traversal of the k-matrix shown in FIG. 3B, so that the measured points 1, 2, 3, 4, 5, 6, 7 and 8 (also indicated in FIG. 3A) come to lie equidistantly in the plane of k-space given a temporally uniform sampling.
The readout of the echo sequence must end at a time that corresponds to the decay of the cross-magnetization. Otherwise, the various rows of the k-matrix would be differently weighted according to the sequence of their acquisition; specific spatial frequencies would be overemphasized but others would be underemphasized. The echo planar technique makes extremely high demands on the gradient system are to the requirement for such high measurement speeds. In practice, for example, gradient amplitudes of about 25 mT/m are employed. Considerable energies must be converted in the shortest possible time, particularly for the repolarization of the gradient field; the switching times, for example, lie in the range of ≦0.3 ms. For power supply, each gradient coil is connected to a gradient amplifier. Since a gradient coil represents an inductive load, correspondingly high output voltages of the gradient amplifier are required for generating the aforementioned currents, and these—as shall be explained below—do not always suffice in order to be able to measure an arbitrary slice in the inside of the basic field magnet.
Such a gradient circuit is technically realized by electronic resonant circuits with an integrated power amplifier that compensates the ohmic losses. Such an arrangement, however, leads to a sinusoidally oscillating gradient field with a constant amplitude.
An EPI pulse sequence with a sinusoidally oscillating readout gradient Gx and a constant phase encoding gradient is shown in FIG. 4A (using the same designations as in FIG. 2A). Given such a sinusoidally oscillating readout gradient Gx, the constant phase encoding gradient Gy leads to a sinusoidal sampling of the k-space, as shown in FIG. 4B (wherein data at points in time 1, 2, 3, 4, 5 and 6 from FIG. 4A are designated). A Fourier transformation by itself is no longer adequate for the later image reconstruction given a sinusoidal sampling of the k-matrix. Additional raster distortion corrections or more general integral transformations must be implemented. Given the same spatial resolution, moreover, the peak value of the gradient amplifier must be higher than for an EPI sequence with trapezoidal gradient pulses as shown in FIG. 3B.
Sequences that include trapezoidal gradient pulses therefore are conventionally employed (see FIGS. 2A, 3A). The amplitude as well as the gradient rate of change (slew rate) of these gradient pulses are based on the amplifier that is used or its performance capability. The slew rate as well as the amplitude of the applied gradient pulse are limited to a maximum value since the amplifier can only generate a specific maximum voltage, and only a limited slew rate of the gradient field can be effected at this maximum voltage due to the inductance of the gradient coil.
Since each coordinate (x-, y-, z-coordinate) has a gradient coil with an appertaining amplifier, this means that the amplitude and the slew rate for each coordinate are limited individually for that coordinate. By combining two or three gradient coils, a field can in fact be generated having an amplitude or slew rate that exceeds the limit values of the respective individual coils. Such a field, however, can be generated only on a diagonal. An individual coil is able to generate a field of this order of magnitude along the axis corresponding to it.
In practical terms for a conventional gradient pulse, this means that the plane of the k-space trajectory that is used to sample the k-matrix cannot be arbitrarily rotated in space without overloading the amplifiers of the corresponding gradient coils. In other words: not every measurement sequence defined by amplitude and slew rate of the respective gradient pulses can be arbitrarily varied such that the measurement ensues in a slice rotated relative to the gradient system without exceeding the amplitude and/or slew rate limit values. Due to the conventional employment of trapezoidal or sinusoidal gradient pulses, it is difficult to avoid, given a rotation of the measurement coordinate system relative to the coordinate system defined by the gradient field directions, exceeding the amplitude and slew rate limits—adhered to by individual pulses—due to vectorial combination.
It is thus a problem in the field of MRT to be able to sample the k-matrix optimally fast but such that the gradient current function can be subjected to an arbitrary rotation without exceeding the amplitude and/or slew rate limits of the individual coils.